The measurement of wall shear stress is important in many flow testing and device applications. Examples include drag measurements on air, space, land, and oceangoing vehicles both in test environments such as wind tunnels and in operation, as well as applications in active flow control. The measurement of surface shear stress is also important in industrial flow applications for fluid handling and manufacturing operations such as extrusion, and for biomedical devices in such applications as tissue engineering, where tissue development may depend on local shear stress. Flow regimes of interest may be as diverse as subsonic and supersonic turbulent boundary layers, turbulent pipe flows, and laminar flow in microchannels. Both steady and unsteady shear forces are of interest, and for some applications, particularly in turbulent boundary layer flows for aeroacoustic and structural acoustic applications, it may be important to capture the fluctuating shear stresses as well as the mean. Ideally, in order to capture the fine structure of turbulence, this would be done with a high spatial resolution on the order of 100 μm or smaller, and with high temporal resolution on the order of/ms or less (Sheplak, et al., (2004); Naughton et al., Prog. Aerospace Sci. 38 (2002) 515-570; Lofdahl et al., Measurement Science & Technology. 10 (1999) 665-686).
A number of techniques exist for measuring surface shear stress. These include oil film interferometry (Tanner, L. Blows, A study of the motion of oil films on surfaces in air flow, with application to the measurement of skin friction, Journal of Physics E: Scientific Instruments. 9 (1976) 194), heated patch or heated wire measurements (Van Oudheusden, Sensors and Actuators A: Physical. 30 (1992) 5-26; Lofdahl et al., Experiments in Fluids. 35 (2003) 240-251; Kalvesten et al., Sensors and Actuators A: Physical. 52 (1996) 51-58), hair-like sensors (Brucker et al., Experiments in Fluids. 39 (2005) 464-474; Dagamseh et al., Bioinspiration & Biomimetics. 7 (2012) 046009; Chen et al., Journal of Aerospace Engineering. 16 (2003) 85), surface fence measurements (Savelsberg et al., Exp. Fluids. 53 (2012) 489-498; von Papen et al., Sensors and Actuators A: Physical. 113 (2004) 151-155), and floating element techniques (see below). These techniques have been reviewed in a number of papers and have various advantages and disadvantages (Sheplak et al., supra; Naughton et al., supra; Winter, Prog. Aerospace Sci. 18 (1979) 1-57; Fernholz et al, Measurement Science and Technology. 7 (1996) 1396; Ho et al., Annu Rev. Fluid Mech. 30 (1998) 579-612).
Microelectromechanical system (MEMS) floating element sensors are one approach to the measurement of wall shear stress. In this measurement technology, a micromachined plate or shuttle is suspended using micromachined beam tethers. Under the influence of hydrodynamic forces, this “floating element” experiences a lateral deflection. The motion may be detected using capacitance change, piezoresistance, or optical methods. MEMS floating elements have the advantages of ease of use, high spatial and temporal resolution, and are a “direct” measurement technology insofar as they respond to momentum transfer at the wall. However, MEMS floating element sensors suffer from some drawbacks, including sensitivity to pressure gradients, potential for misalignment, and a possible lack of robustness to water or particle impingement (Sheplak et al., supra; Naughton et al., supra; Tanner et al., supra).
A number of authors have described these devices in the past. The earliest work on MEMS floating elements is that of Schmidt et al in 1988 (Schmidt et al., IEEE Transactions on. (1988) 750-757). Between 1995 and 1997, major contributions were made by Padmanabhan et al with the introduction of optical detection methods (Padmanabhan et al., The 8th International Conference on Solid State Sensors and Actuators and Eurosensors IX, IEEE (1995)436-439; Padmanabhan et al., Solid State Sensors and Actuators, International Conference on. Vol. 1. IEEE, (1997) 137-140; Padmanabhan et al., Journal of Microelectromechanical Systems. 5 (1996) 307-315). Using optical detection, a resolution of 1 mPa was reported, although most testing occurred at levels below 1 Pa. A single point was recorded by the research group demonstrating linearity to 10 Pa.
Pan et al, Hyman et al, and Patel et al used capacitive sensing for three different related designs that included on-chip electronics and force rebalancing (Hyman et al., AIAA Journal. 37 (1999) 73-78; Pan et al., AIAA Journal. 37 (1999) 66-72; Patel et al., AIAA Journal. 40 (2002) 1582-1588). Linear response was demonstrated out to 4 Pa for the first two designs. The third design is the largest maximum demonstrated linear response in the literature, maintaining linear response out to approximately 25-30 Pa of effective shear stress.
In more recent work, Zhe et al used differential capacitive measurements in a cantilever structure, and focused on high resolution at low stress levels (Zhe, et al., Journal of Microelectromechanical Systems. 14 (2005) 167-175), achieving 0.04 Pa resolution at stresses up to 0.2 Pa. Chandreskaran, et al also used differential capacitive measurement focusing on unsteady shear stress measurement (Chandrasekharan et al., (2009) 1537-1540; Chandrasekharan et al., Microelectromechanical Systems, Journal of. 20 (2011) 622-635), and were able to demonstrate 15 μPa/Hz1/2 resolution at 1 kHz with linear response up to 2 Pa. Notable work by Barlian, et al (Barlian et al., Sensors and Actuators A: Physical. 134 (2007) 77-87) and Shajii, et al (Shajii et al., Microelectromechanical Systems, Journal of 1 (1992) 89-94.) describe piezoresistive floating elements for measurement in liquids.
The majority of MEMS sensors so far described in the literature for measurement in air have either not been calibrated, or not shown linear response, at shear stress levels above 4 Pa, yet average shear stresses on the order of 50 Pa or higher may be routinely encountered in typical air vehicle flow applications. For instance, at a free stream velocity of approximately 250 m/s (Mach 0.8), typical of commercial air liners, in air with sound speed 300 m/s, at a density of 0.4 kg/m3 and a viscosity of 1.5.10-5 Pa·s (approximate properties at a cruise altitude of 10 km), the Reynolds number is 7.106 m-1. The average shear stress under a zero pressure gradient flat plate incompressible turbulent boundary layer at 1 meter from the leading edge will be approximately 40 Pa (Cf=0.003), based on a 1/7th power law skin friction coefficient correlation (White, Viscous Fluid Flow 3rd Edition, McGraw-Hill Education, 2006),
                              C          f                =                              0.027                          Re              x                              1                /                7                                              =                                    τ              w                                      0.5              ⁢                                                          ⁢              ρ              ⁢                                                          ⁢                              U                2                                                                        (        1        )            where Cf is the skin friction coefficient, Rex is the Reynold's number based on distance down a float plate, τw is the wall shear stress, ρ is the density of air and U is the free stream velocity. Compressibility effects at high subsonic Mach numbers will reduce the friction factor by approximately 10% (White, Viscous Fluid Flow 3rd Edition, McGraw-Hill Education, 2006), assuming there is not a great deal of heat transfer from the wall to the flow. These results are consistent with recent oil film measurements on a 2.7% scale model of a commercial airliner, the common research model, conducted in the NASA Ames 11 foot transonic tunnel under similar Mach and Reynold's number conditions to those experience in commercial flight. Measured values of Cf on the majority of the wing, tail, and body varied from approximately 0.002 to 0.004 (Zilliac et al., Proceedings of the Aerospace Sciences Meeting, (2011). AIAA 2011-1129).
Sensors with increased dynamic range, higher spatial resolution, and calibrated sensitivity to pressure gradients are needed.